Derivatives and Graphs

I was having some trouble with a problem. The problem reads:
Sketch the graphs of y = x^2 and y = -x^2+6x-5, and sketch the two lines that are tangent to both graphs. Find equations of these lines.

I've graphed the two parabolas and drew the tangent lines. I've found the derivatives of each equation as well. I relabeled the points where the tangent line is tangent on each of the parabolas using Xsub1 and Xsub2. Am I going about doing this the correct way? Can someone give me a little help, thanks.